Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'.

Front

How do you solve the inequality 6x - 4 ≥ 26?

Back

Add 4 to both sides: 6x ≥ 30. Then divide by 6: x ≥ 5.

Front

When graphing the inequality x > 3, what type of circle is used?

Back

An open circle is used for 'greater than' (>) because the endpoint is not included.

Front

When graphing the inequality x ≤ -2, what type of circle is used?

Back

A closed circle is used for 'less than or equal to' (≤) because the endpoint is included.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips when you multiply or divide both sides by a negative number.

Front

Solve the inequality -3x + 2 ≤ 22. What is x?

Back

Subtract 2 from both sides: -3x ≤ 20. Then divide by -3 (flip the sign): x ≥ -20/3.

Front

What is the solution set for the inequality x < -2?

Back

The solution set includes all numbers less than -2.

Front

How do you represent the solution of the inequality 2x + 3 < 7 on a number line?

Back

Graph a line with an open circle at x = 2 and shade to the left.